What Happens to the Water Level When a Rock is Dropped Overboard?

Physics questions are often the most enjoyable when there is disagreement about the answer. What may seem intuitive or obvious, may not always be the case. These debates can provide hours of entertainment and potentially lead to learning something new.

One example of such a question that has been around for a long time is: If a large rock is dropped from a boat floating in a small pond, will the water level rise, fall, or remain unchanged?

Feel free to engage in this debate with your friends and family. While you try to convince them of your answer, here is a picture of my boat with a rock in it:

Alright, it’s not actually a boat, but rather a part of a plastic bottle. Additionally, the “rock” is a lead weight and the “pond” is a beaker. However, this setup allows us to observe the impact on the water level when an object is dropped into it.

When a boat floats in water, it experiences two forces. First, there is the downward gravitational force, which is equal to the mass of the boat and everything on it (m) multiplied by the gravitational field (g = 9.8 newtons per kilogram). This product is commonly referred to as the “weight.”

The other force is the upward buoyancy exerted by the water. Two important facts about this buoyancy force are: first, it must be equal to the weight of the boat for it to float, and second, it is equal to the weight of the water displaced by the boat.

We can determine the magnitude of this buoyancy force by calculating the volume of water displaced (V_d) and multiplying it by the density of water (ρ_w) and the gravitational field (g).